The best thermoelectric materials are believed to be heavily doped semiconductors. The presence of a band gap is assumed to be essential to achieve large thermoelectric power factor and figure of merit. In this work, we propose semi-metals with large asymmetry between conduction and valence bands as an alternative class of thermoelectric materials. To illustrate the idea, we study semi-metallic HgTe in details experimentally and theoretically. We employ ab initio calculations with hybrid exchange-correlation functional to accurately describe the electronic band structure in conjunction with the Boltzmann Transport theory to investigate the electronic transport properties. We calculate the lattice thermal conductivity using first principles calculations and evaluate the overall figure of merit. To validate our theoretical approach, we prepare semi-metallic HgTe samples and characterize their transport properties. Our first-principles calculations agree well with the experimental data. We show that intrinsic HgTe, a semimetal with large disparity in its electron and hole masses, has a high thermoelectric power factor that is comparable to the best known thermoelectric materials. Finally, we propose other possible materials with similar band structures as potential candidates for thermoelectric applications.

Bismuth is one of the rare materials in which second sound has been experimentally observed. Our exact calculations of thermal transport with the Boltzmann equation predict the occurrence of this Poiseuille phonon flow between ≈1.5 and ≈3.5  K, in a sample size of 3.86 and 9.06 mm, consistent with the experimental observations. Hydrodynamic heat flow characteristics are given for any temperature: heat wave propagation length, drift velocity, and Knudsen number. We discuss a gedanken experiment allowing us to assess the presence of a hydrodynamic regime in any bulk material.